MEMPHIS, Tenn. – The Coast Guard closed a stretch of the swollen Mississippi to barge traffic Friday in a move that could cause a backup along the mighty river, while police farther south in Memphis went door to door, warning thousands of people to leave before they get swamped.

Emergency workers in Memphis handed out bright yellow fliers in English and Spanish that read, “Evacuate!!! Your property is in danger right now.”

All the way south into the Mississippi Delta, people faced the question of whether to stay or go as high water rolled down the Big Muddy and backed up along its tributaries, breaking flood records that have stood since the Depression.

Because of levees and other flood defenses built over the years, engineers said it is unlikely any major metropolitan areas will be inundated as the water pushes downstream over the next week or two, but farms, small towns and even some urban areas could see extensive flooding.

“It’s going to be nasty,” said Bob Bea, a civil engineer at the University of California-Berkeley who investigated levee failures in New Orleans after Hurricane Katrina in 2005. How bad it gets depends on how well the flood protection systems have been built and maintained, he said.

The Coast Guard closed a five-mile stretch of the Mississippi to protect Caruthersville, Mo., and said barges could be banned for up to eight days. The fear was that the wake from big boats would push water over a floodwall and into the town of 6,700.

Barges regularly move coal, grain, ore, gravel, auto parts and other vital products down the Mississippi. A single barge can carry as much material as 70 tractor-trailers, and some towboats can move 45 barges at once.

Lynn Muench, a vice president of the American Waterways Operators, an industry group, said the eight-day shutdown would have a multimillion-dollar effect on the barge industry and slow the movement of many products.

“It’s just like if you took out every bridge going over the Mississippi what that would mean to railroad and vehicle traffic,” Muench said. “You’re shutting down a major thoroughfare.” She added: “The last thing we want is a levee to go, but we also want to keep moving.”

In Tennessee, local authorities were uncertain whether they had legal authority to order evacuations, and hoped the fliers would persuade people to leave. Bob Nations, director of emergency management for Shelby County, which includes Memphis, said there was still time to get out. The river is not expected to crest until Wednesday.

“This does not mean that water is at your doorstep,” Nations said of the door-to-door effort. “This means you are in a high-impact area.”

About 950 households in Memphis and about 135 other homes in Shelby County were getting the notices, Shelby County Division Fire Chief Joseph Rike said. Shelters were opened, and the fliers include a phone number to arrange transportation for people who need it.

Jeanette Twilley of south Memphis came home to find one of the yellow notices on her door. Her house is roughly 75 yards from Nonconnah Creek, which has overflowed its banks and flooded three houses on her street.

“Amazed. Amazed. I just can’t believe this,” said Twilley, who is retired and rents her home. She planned to leave in the afternoon and stay with friends or relatives. “There’s not going to be anybody here,” she said of the neighborhood, a working-class area in one of the poorer sections of Memphis.

In a section of south Memphis outside the evacuation zone, Billy Burke stood in his backyard, where water from a creek has been rising for days. About 20 feet away, a fish jumped out of a pool of standing brown water.

“I’m going to stay as long as I can,” Burke said. “But if the water goes up another 10 feet, I’m out of here.”

Graceland, Elvis Presley’s home and one of the city’s best-known landmarks, is about a 20-minute drive from the river and in no danger of flooding, spokesman Kevin Kern said. “We’re on a hill, high and dry and open for business, and will stay open,” Kern said.

Water pooled at the lowest end of Beale Street, the thoroughfare synonymous with Mississippi blues, but it was about a half-mile from the street’s world-famous nightspots.

The main Memphis airport was not threatened, nor was FedEx, which has a sorting hub at the airport that handles up to 2 million packages per day.

In Missouri, dozens of National Guardsmen and Highway Patrol members who had been rescuing people from floodwaters had to be rescued themselves after six boats got stuck in low water. Half were rescued before dark, and the others spent the night on a levee, relying on provisions dropped to them by the Guard.

“We’re getting our momma and daddy out,” said Ken Gelston, who helped pack furniture, photos and other belongings into pickup trucks in Greenville, Miss. “We could have five feet of water in there,” Gelston said, nodding at the house. “That’s what they’re telling us.”

Bea, the civil engineer, said he is concerned because some levees across the U.S. have been built with inferior dirt, or even sand, and have been poorly designed.

“The standards we use to build these things are on the horribly low side if you judge them by world criteria and conditions,” he said. “The breaches, as we learned in New Orleans, are the killers.”

How long the high water lingers, and how much damage it does to the earthen walls of the levees as it goes down, are crucial factors.

“The whole summer will have to be watched,” said J. David Rogers, a civil engineer at the Missouri University of Science and Technology.

Since the Great Mississippi Flood of 1927, a disaster that killed hundreds, Congress has made protecting the cities on the lower Mississippi a priority. The Army Corps of Engineers has spent $13 billion to fortify cities with floodwalls and carve out overflow basins and ponds — a departure from the “levees-only” strategy that led to the 1927 calamity.

The Corps also straightened out sections of the river that used to meander and pool perilously. As a result, the Mississippi flows into the Gulf of Mexico faster, and water presses against the levees for shorter periods.

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Burdeau reported from Greenville, Miss. Jim Salter in St. Louis and Travis Loller in Nashville, Tenn., contributed to this report.